Question: Solve for $x$ and $y$ using elimination. ${x+2y = 12}$ ${x-3y = 7}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-x-2y = -12}$ $x-3y = 7$ Add the top and bottom equations together. $-5y = -5$ $\dfrac{-5y}{{-5}} = \dfrac{-5}{{-5}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x+2y = 12}\thinspace$ to find $x$ ${x + 2}{(1)}{= 12}$ $x+2 = 12$ $x+2{-2} = 12{-2}$ ${x = 10}$ You can also plug ${y = 1}$ into $\thinspace {x-3y = 7}\thinspace$ and get the same answer for $x$ : ${x - 3}{(1)}{= 7}$ ${x = 10}$